We study a non-cooperative two-sided facility location game in which facilities and clients behave strategically. This is in contrast to many other facility location games in which clients simply visit their closest facility. Facility agents select a location on a graph to open a facility to attract as much purchasing power as possible, while client agents choose which facilities to patronize by strategically distributing their purchasing power in order to minimize their total waiting time. Here, the waiting time of a facility depends on its received total purchasing power. We show that our client stage is an atomic splittable congestion game, which implies existence, uniqueness and efficient computation of a client equilibrium. Therefore, facility agents can efficiently predict client behavior and make strategic decisions accordingly. Despite that, we prove that subgame perfect equilibria do not exist in all instances of this game and that their existence is NP-hard to decide. On the positive side, we provide a simple and efficient algorithm to compute 3-approximate subgame perfect equilibria.

翻译：我们研究了一个非合作的两方设施选址博弈，其中设施与客户均采取策略性行为。这与许多其他设施选址博弈形成鲜明对比，后者中客户仅访问其最近的设施。设施代理人选择图上的位置开设设施，以吸引尽可能多的购买力；而客户代理人则通过策略性地分配其购买力来最小化总等待时间，从而决定光顾哪些设施。其中，设施的等待时间取决于其接收的总购买力。我们证明客户阶段是一个原子可分割拥塞博弈，这意味着客户均衡的存在性、唯一性及高效计算。因此，设施代理人能有效预测客户行为并据此做出策略决策。尽管如此，我们证明该博弈并非在所有实例中存在子博弈完美均衡，且判断其存在性是NP难的。从积极方面看，我们提供了一种简单高效的算法来计算3近似子博弈完美均衡。